Question: Simplify the following expression: $ k = \dfrac{3x - 6}{-5x} - \dfrac{-1}{6} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{3x - 6}{-5x} \times \dfrac{6}{6} = \dfrac{18x - 36}{-30x} $ Multiply the second expression by $\dfrac{-5x}{-5x}$ $ \dfrac{-1}{6} \times \dfrac{-5x}{-5x} = \dfrac{5x}{-30x} $ Therefore $ k = \dfrac{18x - 36}{-30x} - \dfrac{5x}{-30x} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{18x - 36 - 5x }{-30x} $ Distribute the negative sign: $k = \dfrac{18x - 36 - 5x}{-30x}$ $k = \dfrac{13x - 36}{-30x}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{-13x + 36}{30x}$